Abstract: With the tide of globalization, biological invasions and pathogen transmission, which in turn can affect ecosystem or threaten public health, become focal spots in literature. In mathematical biology, there are many reaction-diffusion models arising from various applications such as animal dispersal, geographic spread of epidemics. To model/illustrate these problems/phenomena and investigate/evaluate the corresponding control strategy, it has been proved that the corresponding propagation modes are very important and useful. This minisymposium focus on the recent advances of propagation phenomena of different reaction-diffusion models in biology. In particular, the traveling wave solutions, asymptotic spreading, entire solutions, generalized transmission and threshold dynamics with their applications of reaction-diffusion models will be discussed.

MS-Th-E-03-116:00--16:30Spatial dynamics of a delayed nonlocal reaction-diffusion systemWu, Shiliang (Xidian Univertisty)Abstract: This talk is concerned with the spatial dynamics of a delayed nonlocal reaction-diffusion system. We first investigate the global attractivity of equilibria of the system. Then we establish the exisence of the minimal wave speed of traveling wave solutions and show that it coincides with the spreading speed. Finally, some front-like entire solutions are constructed by combing any finite numbers of traveling wave solutions with different speeds and a spatially independent solution.

MS-Th-E-03-216:30--17:00Traveling wave solutions and entire solutions for nonlocal dispersl equations with delay
Guobao, Zhang (Northwest Normal Univ.)Abstract: In this talk, we study traveling wave solutions and entire solutions for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity. Firstly, by means of the (technical) weighted energy method, we show that the traveling wave with large speed is exponentially stable. Secondly, we apply Ikehara's Tauberian theorem to show that all noncritical traveling waves are unique up to translation. Finally, we combine the traveling wavefronts and spatially independent solutions to construct entire solutions.

MS-Th-E-03-317:00--17:30 On a free boundary problem for a competition system: two invasive species caseWu, Chang-Hong (Department of Applied Mathematics, National Univ. of Tainan)Abstract: We focus on a two-species competition-diffusion model with two free boundaries. Here, two free boundaries which may intersect each other are used to describe the spreading fronts of two competing species, respectively. The spreading mechanism for species is determined by a Stefan condition, which is proposed by Du and Lin (2010). We mainly study the dynamics and offer some biological insight.

MS-Th-E-03-417:30--18:00Persistence and Spread of A Species with A Shifting Habitat EdgeLi, Bingtuan (Univ. of Louisville)Abstract: We discuss a reaction-diffusion model that describes the growth and spread of a species along a shifting habitat gradient. We assume that the linearized species growth rate is positive near positive infinity and is negative near negative infinity. We provide the conditions under which the species goes extinct, and determine the spreading speed at which the species spreads along the shifting habitat gradient. Joint work with Sharon Bewick, Jin Shang, and William F. Fagan.